'To go on' is a phrasal verb and as you rightly said it means 'to take place', 'to occur', 'to happen', sometimes 'to continue'.
'Going on' is a normal participle/gerund form of this verb.
"What's going on here?!", their mother shouted.
He has a lot going on, this man.
I'm sorry I interrupted. Please, do go on.
I am not a teacher.
PS: What is the quote?
Student or Learner